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On the geometrical gyro-kinetic theory. (English) Zbl 1353.37147

Summary: Considering a Hamiltonian dynamical system describing the motion of charged particle in a tokamak or a stellarator, we build a change of coordinates to reduce its dimension. This change of coordinates is in fact an intricate succession of mappings that are built using hyperbolic partial differential equations, differential geometry, Hamiltonian dynamical system theory and symplectic geometry, Lie transforms and a new tool which is here introduced: partial Lie sums.

MSC:

37L50 Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
53D05 Symplectic manifolds (general theory)
82D10 Statistical mechanics of plasmas
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics

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References:

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